The solution of the equation ${\cos ^2}x - 2\cos x = $ $4\sin x - \sin 2x,$ $\,(0 \le x \le \pi )$ is
The solution of the equation ${\cos ^2}x - 2\cos x = $ $4\sin x - \sin 2x,$ $\,(0 \le x \le \pi )$ is
- A
$\pi - {\cot ^{ - 1}}\left( {\frac{1}{2}} \right)$
- B
$\pi - {\tan ^{ - 1}}(2)$
- C
$\pi + {\tan ^{ - 1}}\left( { - \frac{1}{2}} \right)$
- D
None of these
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The value of $\theta $ lying between $0$ and $\pi /2$ and satisfying the equation
$\left| {\,\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{1 + {{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{{{\cos }^2}\theta }&{1 + 4\sin 4\theta }\end{array}\,} \right| = 0$
The value of $\theta $ lying between $0$ and $\pi /2$ and satisfying the equation
$\left| {\,\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{1 + {{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{{{\cos }^2}\theta }&{1 + 4\sin 4\theta }\end{array}\,} \right| = 0$
- [IIT 1988]
$2{\sin ^2}x + {\sin ^2}2x = 2,\, - \pi < x < \pi ,$ then $x = $
$2{\sin ^2}x + {\sin ^2}2x = 2,\, - \pi < x < \pi ,$ then $x = $
Number of values of $x$ satisfying $2sin^22x = 2cos^28x + cos10x$ in $x \in \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is-
Number of values of $x$ satisfying $2sin^22x = 2cos^28x + cos10x$ in $x \in \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is-
If $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is
If $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is
Find the principal solutions of the equation $\tan x=-\frac{1}{\sqrt{3}}.$
Find the principal solutions of the equation $\tan x=-\frac{1}{\sqrt{3}}.$